Connecting Equations to Graphs (Part 2)

ID: nunar-jumar
Created by Illustrative MathIllustrative Math
Subject: Algebra, Algebra 2
Grade: 8-9

Connecting Equations to Graphs (Part 2)

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Problem 1

1) What is the slope of the graph of 5x2y=205x - 2y = 20?

a) 10\text{10}b) 25 \frac{-2}{5} c) 52 \frac{5}{2} d) 5\text{5}
Show Work
Problem 2

What is the yy-intercept of each equation?

2) y=6x+2y = 6x + 2

Show Work

3) 10x+5y=3010x + 5y = 30

Show Work

4) y6=2(3x4)y - 6 = 2(3x - 4)

Show Work
Problem 3

Han wanted to find the intercepts of the graph of the equation 10x+4y=2010x + 4y = 20. He decided to put the equation in slope-intercept form first. Here is his work:

10x+4y=204y=2010xy=510x\begin{array}{rcl} \\[-1em] 10x + 4y &= & 20 \\[-1em] \\ \\[-1em] 4y &= & 20 - 10x \\[-1em] \\ \\[-1em] y &= & 5 - 10x \\[-1em] \\ \end{array}

He concluded that the xx-intercept is (12,0)(\frac{1}{2}, 0) and the yy-intercept is (0,5)(0, 5).

5) What error did Han make?

6) What are the xx-intercepts of the line?

7) Explain or show your reasoning.

8) What is the yy-intercept of the line?

9) Explain or show your reasoning.

Problem 4

10) Which graph represents the equation 12=3x+4y12 = 3x + 4y? Write the letter of the correct graph in the answer box.

A template for answering this question. Ask your instructor for an alternative.
a) Figure A\text{Figure A}b) Figure B\text{Figure B}c) Figure C\text{Figure C}

11) Explain how you know.

Problem 5

Clare knows that Priya has a bunch of nickels and dimes in her pocket and that the total amount is $1.25.

12) Find one possibility for the number of nickels and number of dimes that could be in Priya's pocket.

Show Work

13) Write an equation that describes the relationship between the number of dimes and the number of nickels in Priya's pocket.

14) Explain what the point (13,6)(13, 6) means in this situation.

15) Is the point (13,6)(13, 6) a solution to the equation you wrote?

True or false? Write below.

16) Explain your reasoning.

Problem 6

A large company releases summary statistics about the annual salaries for its employees.

meanstandard deviationminimumQ1medianQ3maximum$63,429$38,439$18,000$50,000$58,000$68,000$350,000\begin{array}{|c|c|c|c|c|c|c|} \hline \\[-1em] \textbf{mean} & \textbf{standard deviation} & \textbf{minimum} & \textbf{Q1} & \textbf{median} & \textbf{Q3} & \textbf{maximum} \\[-1em] \\ \hline \\[-1em] \$63,429 & \$38,439 & \$18,000 & \$50,000 & \$58,000 & \$68,000 & \$350,000 \\[-1em] \\ \hline \end{array}

17) Based on this information, are there any outliers in the data?

True or false? Write below.

18) Explain your reasoning.

Problem 7

The graph shows how much money Priya has in her savings account weeks after she started saving on a regular basis.

A template for answering this question. Ask your instructor for an alternative.

19) How much money does Priya have in the account after 10 weeks?

20) How long did it take her to save $200?

21) How much money did Priya have in her savings account when she started to save regularly?

22) Write an equation to represent the dollar amount in her savings account, dd, and the number of weeks of saving, ww.

23) Specify what each variable represents.

Problem 8

24) Noah has a coin jar containing dd dimes and qq quarters worth a total of $5.00.

Select all the equations that represent this situation. Write each corresponding letter in the answer box and separate letters with commas.

a) d+q=5d + q = 5  b) d+q=500d + q = 500  c) 0.1d+0.25q=50.1d + 0.25q = 5  d) 10d+25q=50010d + 25q = 500 e) d=50d = 50  f) q=20q = 20

Problem 9

25) Noah orders an extra-large pizza. It costs $12.49 for the pizza plus $1.50 for each topping. He orders an extra-large pizza with tt toppings that costs a total of dd dollars.

Select all of the equations that represent the relationship between the number of toppings tt and total cost dd of the pizza with tt toppings. Write each corresponding letter in the answer box and separate letters with commas.

a) 12.49+t=d12.49 + t = d b) 12.49+1.50t=d12.49 + 1.50t = d  c) 12.49+1.50d=t12.49 + 1.50d = t  d) 12.49=d+1.50t12.49 = d + 1.50t  e) t=d12.491.5t = \frac{d - 12.49}{1.5}

f) t=d12.491.5t = d - \frac{12.49}{1.5}

Problem 10

A school sells adult tickets and student tickets for a play. It collects $1,400 in total.

The graph shows the possible combinations of the number of adult tickets sold and the number of student tickets sold.

A template for answering this question. Ask your instructor for an alternative.

26) What does the vertical intercept (0, 200) tell us in this situation?

a) It tells us the decrease in the sale of adult tickets for each student ticket sold.\text{It tells us the decrease in the sale of adult tickets for each student ticket sold.}b) It tells us the decrease in the sale of student tickets for each adult ticket sold.\text{It tells us the decrease in the sale of student tickets for each adult ticket sold.}c) It tells us that if no adult tickets were sold, then 200 students tickets were sold.\text{It tells us that if no adult tickets were sold, then 200 students tickets were sold.}d) It tells us that if no students tickets were sold, then 200 adult tickets were sold.\text{It tells us that if no students tickets were sold, then 200 adult tickets were sold.}